Wand: $$360^{\circ }$$ video projection mapping using a $$360^{\circ }$$ camera

Virtual Reality - In a surrounding projection-based display environment (e.g., a dome theater), the viewers can enjoy a $$360^{\circ }$$ video with a strong sense of immersion. Building a thriving...     

Verification of $${{EB}^3}$$ specifications using CADP

\({{\small {EB}}^3}\) is a specification language for information systems. The core of the \({{\small {EB}}^3}\) language consists of process algebraic specifications describing the behaviour of the entities in a system, and attribute function definitions describing the entity attributes. The verification of \({{\small {EB}}^3}\) specifications against temporal properties is of great interest to users of \({{\small {EB}}^3}\). In this paper, we propose a translation from \({{\small {EB}}^3}\) to LOTOS NT (LNT for short), a value-passing concurrent language with classical process algebra features. Our translation ensures the one-to-one correspondence between states and transitions of the labelled transition systems corresponding to the \({{\small {EB}}^3}\) and LNT specifications. We automated this translation with the \({{{\small {EB}}^3}2{\small {LNT}}}\) tool, thus equipping the \({{\small {EB}}^3}\) method with the functional verification features available in the CADP toolbox.     

Polynomial time $$\rho $$ -locally maximum volume search

Calcolo - The tensor t-function, a formalism that generalizes the well-known concept of matrix functions to third-order tensors, is introduced in Lund (Numer Linear Algebra Appl 27(3):e2288). In...     

Rankboost $$+$$ + : an improvement to Rankboost

Machine Learning - Rankboost is a well-known algorithm that iteratively creates and aggregates a collection of “weak rankers” to build an effective ranking procedure. Initial work on...     

Square roots of $${3\times 3}$$ matrices

We find square roots of a complex-valued matrix \(A_{3 \times 3}\) using equation \(B^{2}=A\). The proposed method is faster than Higham’s method and provides up to 8 square roots with less relative residual and error.     

Tracking of Lines in Spherical Images via Sub-Riemannian Geodesics in $${\text {}}$$

Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an \(L^{\tau }\)-data fidelity term, \(\tau \in \{1,2\}\), are presented. The automated selection of the regularization parameter is based on the discrepancy principle, whereby in each iteration a total variation model has to be minimized. In the case of a locally varying parameter, this amounts to solve a multiscale total variation minimization problem. For solving the constituted multiscale total variation model, convergent first- and second-order methods are introduced and analyzed. Numerical experiments for image denoising and image deblurring show the efficiency, the competitiveness, and the performance of the proposed fully automated scalar and locally varying parameter selection algorithms.     

Singular $$\mathcal{H}$$ 2-optimization problems for discrete-time systems

Singular ₂-optimization problems are considered for the standard discrete-time control system. Two types of singularity (type I and type II) are distinguished. A detailed treatment of problems with singularity of type II, which leads to nonuniqueness of solution, is presented. New algorithms for design of optimal controllers are presented both in frequency domain and state space, which generalize standard procedures onto the case of singular ₂-problems. A parameterization of the set of optimal controllers is given.Translated from Avtomatika i Telemekhanika, No. 3, 2005, pp. 20–33.Original Russian Text Copyright © 2005 by Polyakov.This paper was recommended for publication by B.T. Polyak, a member of the Editorial Board     

Fast LH$$*$$

Linear Hashing is an efficient and widely used version of extendible hashing. LH\(*\) is its distributed version that stores key-value pairs on up to hundreds of thousands of sites in a distributed system. LH\(*\) implements the dictionary data structure efficiently by not using a central component and allows the key-based operations of insertion, deletion, actualization, and retrieval as well as the scan operation. Because it does not use a central addressing component, clients or servers in LH\(*\) can commit an addressing error by sending a request to a wrong server. This server then forwards the message to the correct server either directly or in one but never more than one additional forward operation. We discuss here methods to avoid this double forward, which, while rare, still might breach quality of service guarantees. We compare our methods with \(\mathrm{LH}*_{\mathrm{RS}^{\mathrm{\tiny P2P}}}\) that pushes information about changes in the file structure to clients, whether they are active or not. A second problem especially relevant in high churn environments such as modern data centers is that sites can suddenly become inaccessible. The various high and scalable reliability versions of LH\(*\) then reconstruct the data lost on this site elsewhere. We present a solution to the resulting “wandering bucket” problem that allows clients to find the data at their new location.     

Analyzing the structure of a class of linear automata over a ring $$ Z_{p^k } $$

Basic finite-automaton characteristics are established for the class of all linear automata and information-lossless automata over a ring. The complexities of solving problems of parametric identification and initial-state identification are analyzed. The sets of fixed points for mappings realized by initial automata are characterized. Canonical forms are proposed for linear automata over the ring. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 60–74, May–June 2008.     

Shape Partitioning via $${L}_{p}$$ Compressed Modes

The eigenfunctions of the Laplace–Beltrami operator (manifold harmonics) define a function basis that can be used in spectral analysis on manifolds. In Ozoli et al. (Proc Nat Acad Sci 110(46):18368–18373, 2013) the authors recast the problem as an orthogonality constrained optimization problem and pioneer the use of an \(L_1\) penalty term to obtain sparse (localized) solutions. In this context, the notion corresponding to sparsity is compact support which entails spatially localized solutions. We propose to enforce such a compact support structure by a variational optimization formulation with an \(L_p\) penalization term, with \(0<p<1\). The challenging solution of the orthogonality constrained non-convex minimization problem is obtained by applying splitting strategies and an ADMM-based iterative algorithm. The effectiveness of the novel compact support basis is demonstrated in the solution of the 2-manifold decomposition problem which plays an important role in shape geometry processing where the boundary of a 3D object is well represented by a polygonal mesh. We propose an algorithm for mesh segmentation and patch-based partitioning (where a genus-0 surface patching is required). Experiments on shape partitioning are conducted to validate the performance of the proposed compact support basis.     

Construction of Perfect q-ary Codes by Sequential Switchings of $$\widetilde\alpha $$ -Components

We suggest a construction of perfect q-ary codes using sequential switchings of special-type components of the Hamming code. The construction yields a lower bound on the number of different q-ary codes.     

Super-quantum correlation for SU(2) invariant state in $$4\otimes 2$$ system

We analytically evaluate the weak one-way deficit and super-quantum discord for a system composed of spin-3/2 and spin-1/2 subsystems possessing SU(2) symmetry. We also make a comparative study of the relationships among the quantum discord, one-way deficit, weak one-way deficit, and super-quantum discord for the SU(2) invariant state. It is shown that super-quantum discord via weak measurement is greater than that via von Neumann measurement. But weak one-way deficit is less than the one-way deficit. As a result, weak measurement do not always reveal more quantumness.     

$$\alpha $$ α -Exponential Stability of Impulsive Fractional-Order Complex-Valued Neural Networks with Time Delays

Neural Processing Letters - This paper investigates the global $$\alpha $$ -exponential stability of impulsive fractional-order complex-valued neural networks with time delays. By constructing...     

Robust $$\ell _1$$ Approaches to Computing the Geometric Median and Principal and Independent Components

Robust measures are introduced for methods to determine statistically uncorrelated or also statistically independent components spanning data measured in a way that does not permit direct separation of these underlying components. Because of the nonlinear nature of the proposed methods, iterative methods are presented for the optimization of merit functions, and local convergence of these methods is proved. Illustrative examples are presented to demonstrate the benefits of the robust approaches, including an application to the processing of dynamic medical imaging.     

The randomness in 2$$\rightarrow $$1 quantum random access code without a shared reference frame

The non-classical correlations presented in quantum random access code experiment are a powerful diagnostic tool for semi-device-independent random number generator protocols. The idea behind it is that if the user observes the optimal non-classical correlations, he has the guarantee that the unknown quantum states and measurements in the devices have carefully calibrated (we say have global reference frame), in a relationship which can bring to random outcomes. This means, for observing the non-classical correlations, the devices must have that calibration in previous. However, that calibration can’t always be guaranteed in reality due to unintentional flaws or failures of the quantum apparatuses, thus the devices do not always occur the wanted non-classical correlations. In this paper, we show there will always have non-classical correlations by the proper operations, when the devices have local reference. The quantity of true randomness in the observed non-classical correlations is then quantified by the violation values of some inequality. Besides we also consider the devices without local reference and show the probability of non-classical correlations occurring in 100 trials.     

Proving the distillability problem of two-copy $$4\times 4$$ 4 × 4 Werner states for monomial matrices

Quantum Information Processing - We develop a systematic theory for the construction of quantum codes from classical Reed–Solomon over $${\mathbb {F}}_{p^k}$$ , where p is prime and $$k \in...     

Distant Decimals of $$\pi $$: Formal Proofs of Some Algorithms Computing Them and Guarantees of Exact Computation

We describe how to compute very far decimals of \(\pi \) and how to provide formal guarantees that the decimals we compute are correct. In particular, we report on an experiment where 1 million decimals of \(\pi \) and the billionth hexadecimal (without the preceding ones) have been computed in a formally verified way. Three methods have been studied, the first one relying on a spigot formula to obtain at a reasonable cost only one distant digit (more precisely a hexadecimal digit, because the numeration basis is 16) and the other two relying on arithmetic–geometric means. All proofs and computations can be made inside the Coq system. We detail the new formalized material that was necessary for this achievement and the techniques employed to guarantee the accuracy of the computed digits, in spite of the necessity to work with fixed precision numerical computation.